Seafaring men such as Captain William Bligh of the Bounty and the great circumnavigator Captain James Cook, who made three long voyages of exploration and experimentation before his violent death in Hawaii, took the more promising methods to sea to test their accuracy and practicability.
Renowned astronomers approached the longitude challenge by appealing to the clockwork universe: Galileo Galilei, Jean Dominique Cassini, Christiaan Huygens, Sir Isaac Newton, and Edmond Halley, of comet fame, all entreated the moon and stars for help. Palatial observatories were founded at Paris, London, and Berlin for the express purpose of determining longitude by the heavens. Meanwhile, lesser minds devised schemes that depended on the yelps of wounded dogs, or the cannon blasts of signal ships strategically anchored—somehow—on the open ocean.
In the course of their struggle to find longitude, scientists struck upon other discoveries that changed their view of the universe.

…

The method seemingly answered the dream of laying legible longitude lines on the surface of the globe, except that it was incomplete and inaccurate. Rare was the compass needle that pointed precisely north at all times; most displayed some degree of variation, and even the variation varied from one voyage to the next, making it tough to get precise measurements. What’s more, the results were further contaminated by the vagaries of terrestrial magnetism, the strength of which waxed or waned with time in different regions of the seas, as Edmond Halley found during a two-year voyage of observation.
In 1699, Samuel Fyler, the seventy-year-old rector of Stockton, in Wiltshire, England, came up with a way to draw longitude meridians on the night sky. He figured that he—or someone else more versed in astronomy—could identify discrete rows of stars, rising from the horizon to the apex of the heavens. There should be twenty-four of these star-spangled meridians, or one for each hour of the day.

…

The Prize
Her cutty sark, o’ Paisley harn,
That while a lassie she had worn,
In longitude tho’ sorely scanty,
It was her best, and she was vauntine.
—ROBERT BURNS, “Tam o’ Shanter”
The merchants’ and seamen’s petition pressing for action on the matter of longitude arrived at Westminster Palace in May of 1714. In June, a Parliamentary committee assembled to respond to its challenge.
Under orders to act quickly, the committee members sought expert advice from Sir Isaac Newton, by then a grand old man of seventy-two, and his friend Edmond Halley. Halley had gone to the island of St. Helena some years earlier to map the stars of the southern hemisphere—virtually virgin territory on the landscape of the night. Halley’s published catalog of more than three hundred southern stars had won him election to the Royal Society. He had also traveled far and wide to measure magnetic variation, so he was well versed in longitude lore—and personally immersed in the quest.

In England it arose faint in the early morning sky for a few weeks in November till it approached the sun and faded in the dawn. Few saw it.
A more dramatic spectacle appeared in the nights of December. Newton saw it with naked eye on December 12: a comet whose great tail, broader than the moon, stretched over the full length of King’s College Chapel. He tracked it almost nightly through the first months of 1681.1 A young astronomer traveling to France, Edmond Halley, a new Fellow of the Royal Society, was amazed at its brilliance.2 Robert Hooke observed it several times in London. Across the Atlantic Ocean, where a handful of colonists were struggling to survive on a newfound continent, Increase Mather delivered a sermon, “Heaven’s Alarm to the World,” to warn Puritans of God’s displeasure.3
Halley served as a sometime assistant to a new officeholder, the Astronomer Royal.

…

I doubt not but that by your excellent method you will easily find out what that Curve must be, and its proprietys, and suggest a physicall Reason of this proportion.21
Hooke had finally formulated the problem exactly. He acknowledged Newton’s superior powers. He set forth a procedure: find the mathematical curve, suggest a physical reason. But he never received a reply.
Four years later Edmond Halley made a pilgrimage to Cambridge. Halley had been discussing planetary motion in coffee-houses with Hooke and the architect Christopher Wren. Some boasting ensued. Halley himself had worked out (as Newton had in 1666) a connection between an inverse-square law and Kepler’s rule of periods—that the cube of a planet’s distance from the sun varies as the square of its orbital year. Wren claimed that he himself had guessed at the inverse-square law years before Hooke, but could not quite work out the mathematics.

…

He did not restrict himself to idealized tides but tried to consider the geography of estuaries and rivers. He studied the map of Batsha Harbor, with multiple inlets and open channels, reaching the China Sea and the Indian Ocean, and worked out a theory of wave interference that could account for the data. I. Bernard Cohen, “Prop. 24: Theory of the Tides; The First Enunciation of the Principle of Interference,” in Principia 240; Ronan, Edmond Halley, pp. 69f.
29. Galileo, Dialogue, pp. 445 and 462.
30. These explicitly became rules in the second edition; in the first, they were called “hypotheses.” Principia 794–96. There were four rules in all; the others were:
Those qualities of bodies that cannot be increased or diminished and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.

Pythagoras, shown below, is credited with being the first to find this connection, “one of the truly momentous discoveries in the history of mankind.”
Newton’s theory of gravity propelled him to instant fame. He liked to tell the story, depicted in this Japanese print, that the crucial insight came from watching an apple fall. The story is quite likely a myth. Before anyone knew of his mathematical genius, Newton had dazzled the Royal Society with this compact yet powerful telescope.
Edmond Halley (known today for Halley’s Comet) was a brilliant astronomer and, just as surprisingly, a man so congenial that he could get along with Isaac Newton. Halley took on the task of coaxing the reluctant, secretive Newton into publishing his masterpiece, Principia Mathematica. The 500-page book, in Latin and dense with mathematics, might never have appeared without Halley’s labors.
Newton’s tomb, in Westminster Abbey.

…

Stymied by the difficulty of sorting out gravity, or perhaps tempted more by questions in other fields, Newton had put gravity aside after his miracle years. He had made his apple-and-moon calculation when he was in his twenties. For the next twenty years he gave most of his attention to optics, alchemy, and theology instead.
Late on a January afternoon in 1684, Robert Hooke, Christopher Wren, and Edmond Halley left a meeting of the Royal Society and wandered into a coffeehouse to pick up a conversation they had been carrying on all day. Coffee had reached England only a generation before, but coffeehouses had spread everywhere.49 Hooke in particular seemed to thrive in the rowdy atmosphere. In crowded rooms thick with the hubbub of voices and the smells of coffee, chocolate, and tobacco, men sat for hours debating business, politics, and, lately, science.

…

Much of Newton’s work in Book II was to show that Descartes’ model was incorrect. Whirlpools would eventually fizzle out. Rather than carry a planet on its eternal rounds, any whirlpool would sooner or later be “swallowed up and lost.” In any case, no such picture could be made to fit with Kepler’s laws.
Then came Book III, which was destined to make the Principia immortal.
Chapter Forty-Eight
Trouble with Mr. Hooke
If not for the Principia’s unsung hero, Edmond Halley, the world might never have seen Book III. At the time he was working to coax the Principia from Newton, Halley had no official standing to speak of. He was a minor official at the Royal Society—albeit a brilliant scientist—who had taken on the task of dealing with Newton because nobody else seemed to be paying attention. Despite its illustrious membership, the Royal Society periodically fell into confusion.

Speaking at a ceremony honoring the centenary of Einstein’s birth, the Pope declared that Galileo had “suffered at the hands of men and institutions of the Church,” adding that “research performed in a truly scientific manner can never be in contrast with faith because both profane and religious realities have their origin in the same God.”32
6
NEWTON’S REACH
Watch the stars, and from them learn.
To the Master’s honor all must turn,
each in its track, without a sound,
forever tracing Newton’s ground.*
—Einstein
Nearer the gods no mortal may approach.
—Edmond Halley,
on Newton’s Principia
Newton created a mathematically quantified account of gravitation that embraced terrestrial and celestial phenomena alike. In doing so he demolished the Aristotelian bifurcation of the universe into two realms, one above and one below the moon, and established a physical basis for the Copernican universe. The thoroughness and assurance with which he accomplished this task were such that his theory came to be regarded, for more than two centuries thereafter, as something close to the received word of God.

…

We feel certain that the forms and qualities of things can best be explained by the principles of mechanics, and that all effects of Nature are produced by motion, figure, texture, and the varying combinations of these and that there is no need to have recourse to inexplicable forms and occult qualities, as to a refuge from ignorance.10
This clear new cast of mind was personified by the three members of the Royal Society—Edmond Halley, Christopher Wren, and Robert Hooke—who lunched together in a London tavern one cold January afternoon in 1684. Wren, who had been president of the Royal Society, was an astronomer, geometer, and physicist, and the architect of St. Paul’s Cathedral—where his body is entombed, with an epitaph composed by his son inscribed on the cathedral wall that reads, IF YOU SEEK A MONUMENT, LOOK AROUND. Hooke was an established physicist and astronomer, the discoverer of the rotation of Jupiter; it was he who had worded the society’s credo: “To improve the knowledge of natural things, and all useful Arts, Manufactures, Mechanic practices, Engines and Inventions by Experiments (not meddling with Divinity, Metaphysics, Morals, Politics, Grammar, Rhetoric or Logic).”11 Halley at twenty-seven years old was a generation younger than his two companions, but he had already made a name for himself in astronomy, charting the southern skies from the island of St.

…

Venus comes closer to Earth than does Mars, and so should be still more accessible to triangulation, but when closest it is lost in the glare of the sun. Twice in a long while, however, in pairs of events separated by just over a century, Venus passes directly in front of the sun. During these transits, as they are called, the planet appears as a black circle silhouetted against the blazing solar disk. Edmond Halley, who had observed a transit of Mercury during his expedition to St. Helena, realized that the distance to Venus might be determined by timing, from widely separated stations, exactly when the planet appeared and disappeared from the face of the sun. The edge of the sun would serve as a clearly defined backdrop, the planet as a kind of surveyor’s stake out in space.
Halley knew that he would not live to observe a transit of Venus.

Why didn't the French make their measurements in France and save themselves all the bother and discomfort of their Andean adventure?
The answer lies partly with the fact that eighteenth-century scientists, the French in particular, seldom did things simply if an absurdly demanding alternative was available, and partly with a practical problem that had first arisen with the English astronomer Edmond Halley many years before—long before Bouguer and La Condamine dreamed of going to South America, much less had a reason for doing so.
Halley was an exceptional figure. In the course of a long and productive career, he was a sea captain, a cartographer, a professor of geometry at the University of Oxford, deputy controller of the Royal Mint, astronomer royal, and inventor of the deep-sea diving bell.

…

At his urging, the Royal Society agreed to engage a reliable figure to tour the British Isles to see if such a mountain could be found. Maskelyne knew just such a person—the astronomer and surveyor Charles Mason. Maskelyne and Mason had become friends eleven years earlier while engaged in a project to measure an astronomical event of great importance: the passage of the planet Venus across the face of the Sun. The tireless Edmond Halley had suggested years before that if you measured one of these passages from selected points on the Earth, you could use the principles of triangulation to work out the distance to the Sun, and from that calibrate the distances to all the other bodies in the solar system.
Unfortunately, transits of Venus, as they are known, are an irregular occurrence. They come in pairs eight years apart, but then are absent for a century or more, and there were none in Halley's lifetime.*5 But the idea simmered and when the next transit came due in 1761, nearly two decades after Halley's death, the scientific world was ready—indeed, more ready than it had been for an astronomical event before.

…

Even the Reverend Buckland, as pious a soul as the nineteenth century produced, noted that nowhere did the Bible suggest that God made Heaven and Earth on the first day, but merely “in the beginning.” That beginning, he reasoned, may have lasted “millions upon millions of years.” Everyone agreed that the Earth was ancient. The question was simply how ancient.
One of the better early attempts at dating the planet came from the ever-reliable Edmond Halley, who in 1715 suggested that if you divided the total amount of salt in the world's seas by the amount added each year, you would get the number of years that the oceans had been in existence, which would give you a rough idea of Earth's age. The logic was appealing, but unfortunately no one knew how much salt was in the sea or by how much it increased each year, which rendered the experiment impracticable.

The fact that Newton took every opportunity to insult Hooke, his statement that his own theory destroyed “all he [Hooke] has said,” and his refusal to take his own book on light, Opticks, to the press until after Hooke’s death, argue that this interpretation of the quote may not be too far-fetched. The feud between the two scientists reached an even higher peak when it came to the theory of gravity. When Newton heard that Hooke had claimed to be the originator of the law of gravity, he meticulously and vindictively erased every single reference to Hooke’s name from the last part of his book on the subject. To his friend the astronomer Edmond Halley (1656–1742), Newton wrote on June 20, 1686:
Figure 27
He [Hooke] should rather have excused himself by reason of his inability. For tis plain by his words he knew not how to go about it. Now is not this very fine? Mathematicians that find out, settle and do all the business must content themselves with being nothing but dry calculators and drudges and another that does nothing but pretend and grasp at all things must carry away all the invention as well of those that were to follow him as of those that went before.

…

His observation that the percentages of certain events previously considered purely a matter of chance or fate (such as deaths caused by various diseases) in fact showed an extremely robust regularity, introduced scientific, quantitative thinking into the social sciences.
The researchers who followed Graunt adopted some aspects of his methodology, but also developed a better mathematical understanding of the use of statistics. Surprisingly perhaps, the person who made the most significant improvements to Graunt’s life table was the astronomer Edmond Halley—the same person who persuaded Newton to publish his Principia. Why was everybody so interested in life tables? Partly because this was, and still is, the basis for life insurance. Life insurance companies (and indeed gold diggers who marry for money!) are interested in such questions as: If a person lived to be sixty, what is the probability that he or she would also live to be eighty?
To construct his life table, Halley used detailed records that were kept at the city of Breslau in Silesia since the end of the sixteenth century.

…

There was no question that mathematical truths existed in their own world and that the human mind could access these verities without any observation, solely through the faculty of reason. The first signs of a potential gap between the perception of Euclidean geometry as a collection of universal truths and other branches of mathematics were uncovered by the Irish philosopher George Berkeley, Bishop of Cloyne (1685–1753). In a pamphlet entitled The Analyst; Or a Discourse Addressed to An Infidel Mathematician (the latter presumed to be Edmond Halley), Berkeley criticized the very foundations of the fields of calculus and analysis, as introduced by Newton (in Principia) and Leibniz. In particular, Berkeley demonstrated that Newton’s concept of “fluxions,” or instantaneous rates of change, was far from being rigorously defined, which in Berkeley’s mind was sufficient to cast doubt on the entire discipline:
The method of fluxions is the general key, by help whereof the modern Mathematicians unlock the secrets of Geometry, and consequently of Nature…But whether this Method be clear or obscure, consistent or repugnant, demonstrative or precarious, as I shall inquire with the utmost impartiality, so I submit my inquiry to your own Judgement, and that of every candid Reader.

By the seventeenth century, however, cumulative experience suggests the phenomenon may be exploitable. Perhaps the degree of “variation” of the compass can be measured from place to place, and the featureless oceans resolved into magnetic zones to help sailors establish their whereabouts during weeks or months at sea. This possibility launches the first purely scientific voyage, under the command of Edmond Halley, the only Astronomer Royal ever to win a commission as captain in the Royal Navy.
Between 1698 and 1700, Halley leads two expeditions across the Atlantic Ocean, and also to the Atlantic’s northern and southern limits until stopped by icebergs in fog. Off the coast of Africa and again near Newfoundland, Halley’s specially designed flat-bottomed vessel, the Paramore, draws friendly fire from English merchantmen and colonial fishermen who mistake her for a pirate ship.

In fact, few astronomers even seemed interested in it until then.
In 1952 the great Anglo-Austrian cosmologist Hermann Bondi published an influential textbook in which the term “Olbers’ Paradox” was coined for the first time. But as we shall see, the attribution was misplaced, for Olbers was not the first to pose the problem, nor was his contribution to its resolution particularly original or enlightening. A century before him Edmond Halley had already stated it, and a century before him Johannes Kepler had posed it in 1610. And even he wasn’t the first to record it: for that, we have to go back to 1576 and the very first English translation of De revolutionibus, the great work of Copernicus, written a few decades earlier.
Any account of the history of astronomy begins with the same few key individuals in the leading roles. First up is Ptolemy, the second-century Greek who, despite writing one of the most important scientific textbooks in history (known as the Almagest), believed erroneously that the Sun revolved around the Earth.

…

What Digges was missing was a vital mathematical calculation that would have shown the error in his reasoning about the darkness of the night sky. But that was to come later. In 1610 Johannes Kepler revisited the problem, arguing the reason it was dark at night was simply because the Universe was finite in extent: the darkness between the stars was the dark outer wall enclosing the Universe. Over a century after Kepler, another astronomer, the Englishman Edmond Halley, looked at the problem again and came out in support of Digges’ original solution: that the Universe is infinite, but that the distant stars are too faint to be seen.
Figure 3.1 Three models of the Universe
It was a Swiss astronomer by the name of Jean-Philippe de Chéseaux who showed, a few years later, that this does not help resolve the problem. He proved, using some neat geometry, that if we imagine all the stars grouped into concentric shells around us, like the layers of an onion, extending out to infinity—and assuming that on average the stars are all of the same brightness2 and are distributed evenly throughout the Universe (which we know is not the case, but is nevertheless an acceptable assumption to make for the purposes of this proof)—then, while the stars in the innermost shells will shine most brightly, the shells farther out, which because they are larger in volume contain more stars, have an overall brightness that is exactly equal to any of the inner shells.

The most famous is in the northern constellation Andromeda, the mythical princess situated in the sky near her parents, Cassiopeia and Cepheus, and her husband, Perseus. At her waist is an oval patch of light, best seen on the darkest of nights. As early as the tenth century, astronomer Al-Sufi of Persia noted it as a “little cloud” in his catalog of the heavens. With the invention of the telescope more nebulae were sighted, and by the early 1700s Edmond Halley (of comet fame) counted six in all. To some observers, these pale entities were breaks in the celestial sphere, through which the light of the Empyrean—the highest heaven—came shining down. Others suggested that they were the hazy atmospheres surrounding distant stars. Halley, however, thought of them as unique celestial objects, unlike anything else in the heavens. They “appear to the naked Eye like small Fixed Stars,” he wrote, “but in reality are nothing else but the Light coming from an extraordinary great Space in the Ether; through which a lucid Medium is diffused, that shines with its own proper Lustre.”

…

To Millikan, Hubble was a “man of magnificent physique, admirable scholarship, and worthy and lovable character…. I have seldom known a man who seemed to be better qualified to meet the conditions imposed by the founder of the Rhodes scholarship than is Mr. Hubble.”
Hubble arrived at Oxford in October 1910, living for the next three years on an annual stipend of fifteen hundred dollars. There he walked the very halls where Edmond Halley once strode and joined a cozy club of privileged young men from England's wealthiest families, who were training for select positions in the military, banking, industry, government, and diplomatic services. With continued pressure from both his father and grandfather, Hubble dutifully studied the law and completed the jurisprudence coursework in two years instead of the usual three. He received second-class honors.

…

., p. 84.
40 “there may be innumerable other spheres”: Swedenborg (1845), pp. 271–72.
40 what they thought he meant: See Hoskin (1970).
40 “just universes and, so to speak, Milky Ways”: Kant (1900), p. 63.
41 Kant's manuscript was destroyed: Hetherington (1990b), p. 15.
41 “I easily persuaded myself”: Kant (1900), p. 33.
41 “island universes”: The phrase was never used by Kant. Humboldt first applied the term to describe Kant's theory in his book Kosmos, published in 1845. He wrote it in his native language as Weltinsel, “world island,” which was later transformed into the more familiar expression.
41 Edmond Halley (of comet fame) counted six in all: Not all of the objects on Halley's list were true nebulae. The six are: (1) the Orion nebula, (2) the Andromeda nebula (now galaxy), (3) the globular cluster M22 in Sagittarius, (4) the globular cluster Omega Centauri, (5) the open star cluster M11 in Scutum, and (6) the globular cluster M13 in Hercules. In Halley's day, all appeared as unresolved clouds through a telescope.
42 “appear to the naked Eye”: Halley (1714–16), p. 390.
42 Charles Messier published in France his famous list of more than one hundred nebulae: Messier (1781).
42 “I … saw, with the greatest pleasure”: Herschel (1784b), pp. 439–40.
42 “These curious objects”: Herschel (1789), p. 212.
43 “may well outvie our milky-way in grandeur”: Herschel (1785), p. 260.
43 “When I read of the many charming discoveries”: Bennett (1976), p. 75.
43 Caroline, who had earlier joined him in England, fed him morsels of food by hand: Caroline Herschel was more than her brother's handmaiden; she was an accomplished astronomer in her own right.

And a firm figure for the Earth-Sun distance would constitute a crucial milestone en route to the stars.
An opportunity to define the much desired Earth-Sun distance, or astronomical unit, arose late in the eighteenth century, on the occasion of the 1761 transit of Venus. Twice in about a hundred years, the orbits of Earth and Venus allow the sister planet to be seen crossing the face of the Sun over a period of several hours. English astronomer royal Edmond Halley foresaw the phenomenon’s potential for resolving the distance dilemma. He imagined observers venturing far to the north and south of the globe to watch the transit and record the exact times of its various stages. The wide geographical separation between the observing parties would cause each to see Venus transit the Sun at a slightly different solar latitude. Later, by comparing their notes and triangulating, they could deduce the distance to Venus and extrapolate the Earth-Sun distance.

…

CHAPTER FIVE: Bailey’s Pictures from Peru
Annie Jump Cannon was a lifelong diarist and prolific letter writer. Her diaries, scrapbooks, and other papers, including the libretti she collected for the many opera performances she attended, are held in the Harvard University Archives.
Antonia Maury’s “Verses to the Vassar Dome,” written in 1896, were printed in Popular Astronomy in 1923.
Edmond Halley summoned astronomers to observe the transit of Venus with his announcement, in Latin, of “A New Method of Determining the Parallax of the Sun,” published in Philosophical Transactions of the Royal Society in 1716.
CHAPTER SIX: Mrs. Fleming’s Title
The handwritten Journal of Williamina Paton Fleming, part of the Harvard “Chest of 1900,” is held in the University Archives and can be read online at http://pds.lib.harvard.edu/pds/view/3007384.

Indeed, navigators found that the compass became ever more erratic as a ship moved farther north. Still, it might be possible to record these variations at many points on land and sea and thus create a magnetic chart of longitude.
In 1698 Queen Mary II of England bankrolled the effort to create such a chart. The royal treasury financed the construction of a small vessel and chose eminent mathematician and astronomer Edmond Halley to lead the expedition. Over two years and two voyages, Halley and his team carefully collected magnetic data over a vast area of the Atlantic Ocean, from 52 degrees north of the equator to 52 degrees south. The result was the first magnetic declination chart.
Halley’s chart, and many that have been created since, is a superb resource for navigators, enabling them to correct their compass readings.

…

A thematic map can teach you a great deal about a region at a glance. To make a thematic map, you must start with a reasonably accurate geographic map. Then you overlay this map with “georeferenced” data, which are facts about some aspect of the world that are associated with a specific place. For instance, knowing which way the wind will blow is vital data for those who rely on sailing ships to get around. The renowned astronomer Edmond Halley collected thousands of wind measurements taken at various places on the world’s oceans and transcribed the data onto a map. The result was the first map of global wind patterns, a valuable aid to navigators published by Halley in 1686.
In the seventeenth century European scholars understood the value of collecting and cataloging data on every imaginable subject. As their databases became deeper and more geographically precise, cartographers painted layers of valuable georeferenced information onto more and more maps.

Second, between October 1642 and October 1644, Johannes Hevelius of Danzig made daily drawings of the sun that recorded the precise location of all spots, and he later printed his findings in a series of 26 ‘composite disks’ that showed not only the number but also the movement of the spots over a few days (Plate 1). Hevelius's ‘disks’ reveal that sunspots were already rare: he seldom saw more than one or two groups at a time. Third, the aurora borealis (the ‘northern lights’ caused when highly charged electrons from the magnetosphere interact with elements in the earth's atmosphere) became so rare that when the astronomer Edmond Halley saw an aurora in 1716 he wrote a learned paper describing the phenomenon – because it was the first he had seen in almost fifty years of observation.37 Finally, neither Halley nor other astronomers between the 1640s and the 1700s mentioned the brilliant corona nowadays visible during a total solar eclipse: instead they reported only a pale ring of dull light, reddish and narrow, around the moon.

…

Everyone, they found, was ‘well acquainted with writings of all the learned and ingenious men’ of Europe, whether dead (such as Bacon, Harvey, Galileo and Descartes) or alive (they named Robert Boyle, Thomas Hobbes and Robert Hooke).61
The ‘Republic of Letters’ also included practitioners who lived east of the Elbe and south of the Pyrenees. The Danzig brewer and astronomer Johannes Hevelius, who in 1647 published the lavishly illustrated Selenographia, the first lunar atlas (see Plate 1), had studied at Leiden and met scholars in England and France; became a Fellow of the Royal Society; and welcomed Edmond Halley and other prominent scientists to his impressive observatory in Danzig. In Spain, Miguel Marcelino Boix y Moliner asserted in a book entitled Hippocrates illuminated (1716) that ‘the foreign doctors and philosophers of the last century’ had only managed to ‘make great advances’ thanks to plagiarizing their Spanish precursors. He singled out the work of ‘Gideon’ Harvey on the circulation of the blood, ‘Renato’ Descartes on philosophy, and Richard Morton on cinchona bark, all of whom (he claimed) had simply replicated the earlier research by Spanish scholars – three little-known examples of ‘contested multiples’.

…

He predicted that ‘such a work would be of greater public utility than it might seem at first sight’, but (he continued with a sigh) ‘I have no hope that anyone will do it’ because ‘I think it is a skill beyond the reach of the human mind’. Isaac Newton took up this challenge in the 1680s, carefully copying into his notebooks the descriptions of comets that he found in Aristotle, medieval chronicles and more modern accounts, as well as the observations made by his contemporaries – not only Edmond Halley (who travelled to several European observatories to check their records) and John Flamsteed (the astronomer royal) but also the Jesuit Valentin Stansel from Brazil, the Harvard astronomer Thomas Brattle and his former schoolmate Arthur Storer, now a planter slave-owner in Calvert County, Maryland, who transmitted outstanding observations of the 1682 comet. Newton incorporated these and other findings gleaned from informants all around the world in his remarkable Mathematical Principles of 1687, of which the third book (entitled ‘The System of the World’) contained a long section about comets (Fig. 55).72 Newton also used his newly invented mathematical technique, later known as calculus, to plot the course of the 1680 comet and concluded that it had come from outer space on a parabolic curve around the sun and would never return.

Newton soon clashed with the Astronomer Royal, John Flamsteed, who had earlier provided Newton with much-needed data for Principia, but was now withholding information that Newton wanted. Newton would not take no for an answer: he had himself appointed to the governing body of the Royal Observatory and then tried to force immediate publication of the data. Eventually he arranged for Flamsteed’s work to be seized and prepared for publication by Flamsteed’s mortal enemy, Edmond Halley. But Flamsteed took the case to court and, in the nick of time, won a court order preventing distribution of the stolen work. Newton was incensed and sought his revenge by systematically deleting all references to Flamsteed in later editions of Principia.
A more serious dispute arose with the German philosopher Gottfried Leibniz. Both Leibniz and Newton had independently developed a branch of mathematics called calculus, which underlies most of modern physics.

De Witt sought to quantify the very risk that purchasers of annuities insured themselves against. To solve the problem, De Witt basically estimated survival probabilities according to age and then proposed an age-dependent pricing scale. It was a coarse simplification, but a significant step toward a solution. A more precise answer to the annuity valuation problem would actually emerge from something quite strange: games and play.
15
THE DISCOVERY OF CHANCE
Edmond Halley’s graphic representation of the mortality probabilities for a tontine with three claimants.
The annuity contract was one of Europe’s greatest contributions to humanity. By purchasing an annuity on a single life, or an annuity on a group of lives, citizens could shift the risk of longevity or untimely death from the family to the state. This allowed the state to pool together the risks of many families, which in turn made everyone better off.

…

Caspar Naumann made a careful study of the city records of Breslaw in the 1690s. These records provided copious details about the births and deaths in the Silesian port city from 1687 to 1691—enough information to reliably estimate the life expectancy for various age groups. Instead of sharing this data with Bernoulli, Leibnitz forwarded it to the Royal Academy in London, where it piqued the interest of the astronomer, Edmund Halley. Halley used the Breslaw data to construct mortality tables, that is, frequencies of death by age group. He published his findings in 1693 in the Transactions of the Royal Academy.5 Perhaps most importantly, Halley used statistical analysis to show that the government was selling their life annuities way too cheaply.
Life annuities in England during Halley’s time cost the same for the young as for the old.

Kepler, on the other hand, lectured on astronomy in schools, published extensively and often at his own expense, and wrote science fiction, which was certainly not intended primarily for his scientific peers. He may not have been a popular writer of science in the modern sense, but the transition in attitudes in the single generation that separated Tycho and Kepler is telling.
*Sadly, Newton does not acknowledge his debt to Kepler in his masterpiece the Principia. But in a 1686 letter to Edmund Halley, he says of his law of gravitation: “I can affirm that I gathered it from Kepler’s theorem about twenty years ago.”
CHAPTER IV
HEAVEN AND HELL
The doors of heaven and hell are adjacent and identical.
—Nikos Kazantzakis, The Last Temptation of Christ
The Earth is a lovely and more or less placid place. Things change, but slowly. We can lead a full life and never personally encounter a natural disaster more violent than a storm.

…

Comets shine, as the planets do, by reflected sunlight, “and they are much mistaken who remove them almost as far as the fixed stars; for if it were so, the comets could receive no more light from our Sun than our planets do from the fixed stars.” He showed that comets, like planets, move in ellipses: “Comets are a sort of planets revolved in very eccentric orbits about the Sun.” This demystification, this prediction of regular cometary orbits, led his friend Edmund Halley in 1707 to calculate that the comets of 1531, 1607 and 1682 were apparitions at 76-year intervals of the same comet, and predicted its return in 1758. The comet duly arrived and was named for him posthumously. Comet Halley has played an interesting role in human history, and may be the target of the first space vehicle probe of a comet, during its return in 1986.
Modern planetary scientists sometimes argue that the collision of a comet with a planet might make a significant contribution to the planetary atmosphere.

…

The cometary orbit is 2пa = 2п × 105 × 1.5 × 108 km ≈ 1014 km around, and its speed is therefore only 1014 km/1015 sec = 0.1 km/sec ≈ 220 miles per hour.
*On Mars, where erosion is much more efficient, although there are many craters there are virtually no ray craters, as we would expect.
*As far as I know, the first essentially nonmystical attempt to explain a historical event by cometary intervention was Edmund Halley’s proposal that the Noachic flood was “the casual Choc [shock] of a Comet.”
†The Adda cylinder seal, dating from the middle of the third millennium B.C., prominently displays Inanna, the goddess of Venus, the morning star, and precursor of the Babylonian Ishtar.
*It is, incidentally, some 30 million times more massive than the most massive comet known.
*Light is a wave motion; its frequency is the number of wave crests, say, entering a detection instrument, such as a retina, in a given unit of time, such as a second.

The process of “discounting” is central to financial analysis today—from businesses working out whether to invest in a new plant to pension schemes assessing whether they have enough money to pay their members’ retirement benefits—and is connected to Fibonacci by an eight-hundred-year thread.12
If Fibonacci’s contribution to finance is little known compared to his more famous observation, the same goes for Edmond Halley. Another of the great polymaths that previous ages routinely turned out, Halley was an English astronomer royal who gave his name to the comet that is visible from earth every seventy-five to seventy-­six years (its next visit is due in 2061). The comet won him immortality, but his major financial breakthrough was concerned with death. Halley developed the first proper “life table,” which used demographic data from the German city of Breslau to calculate how many people in the city were alive at every age up to eighty-four.

One of the young men who acquired a taste for coffeehouse discussions while studying at Oxford was the English architect and scientist Christopher Wren. Chiefly remembered today as the architect of St. Paul's Cathedral in London, Wren was also one of the leading scientists of his day. He was a founding member of the Royal Society, Britain's pioneering scientific institution, which was formed in London in 1660. Its members, including Hooke, Pepys, and Edmond Halley (the astronomer after whom the comet is named), would often decamp to a coffeehouse after the society's meetings to continue their discussions. To give a typical example, on May 7, 1674, Hooke recorded in his diary that he demonstrated an improved form of astronomical quadrant at the Royal Society, and repeated his demonstration afterward at Garraway's coffeehouse, where he discussed it with John Flamsteed, an astronomer appointed by Charles II as the first astronomer royal the following year.

An ancient man on his last legs might somehow survive another decade, while his grandson, beaming with youth and health, not live to see the following spring.
Stories took the place of science, their tellers repeating the same message over and over: life is full of surprises. Remember Old John, one tale would go, Old John who laughed so hard at his neighbour’s joke that his heart gave out? The farmer’s wife who was butted into her grave by the goat? The squire who caught cold sleeping in church?
It was in this atmosphere of ambivalence that Edmond Halley, who found lasting fame calculating a comet’s orbit, published An Estimate of the Degrees of the Mortality of Mankind in 1693. Halley based his figures on the city of Breslaw, capital of the province of Silesia, ‘near the confines of Germany and Poland and very near the latitude of London’ with a total population of 34,000. For five years running, monthly figures for every birth and death in the city had been collated: 6,193 births and 5,869 burials in all.

If Isaac Newton owned a copy of On the Revolutions, it has not survived. In his student days, he undoubtedly consulted one of the three Trinity College first editions still held by that venerable library. After Newton established universal gravitation as the force that kept the planets in their orbits around the Sun, copies of Copernicus’s book came into the possession of many other giants in astronomy, such as comet namesake Edmond Halley, his successor as astronomer royal George Biddell Airy, computing pioneer Charles Babbage, and twentieth-century cosmologist Edwin Hubble, who was first to appreciate the infinite extent and continuing expansion of the universe.
Now that Copernicus’s text no longer serves to describe the known paths of the planets, it is more highly valued than ever as an icon. The most recent copy of the book offered at auction—a clean, unannotated first edition—sold at Christie’s, New York, in June 2008 (to an undisclosed recipient) for $2,210,500.

And how much should you pay?
In the late 1990s, the way most bond investors and lending banks looked at credit was reminiscent of how insurance companies work. This safety-in-numbers actuarial approach went back three hundred years, to a financial breakthrough that transformed the way people dealt with misfortune: the birth of modern life insurance. The early life insurance companies were based on the work of Edmund Halley, who published the first usable mortality tables, based on parish records for the Polish-German city of Breslau, in 1693, showing that about one in thirty inhabitants of the city died each year. Armed with these figures, a company could use the one-thirtieth fraction to set prices for life insurance policies and annuities. Policyholders were members of a population subject to patterns of death and disease that could be measured, averaged, and thus risk-managed.

…

In using this new mathematics to ask how likely such events were, Bernoulli and de Moivre laid the foundations for statistical testing and, ultimately, value at risk (VAR).
Driven as ever by financial insecurity, de Moivre seized on the commercial applications of this theory for the next thirty years. Later editions of the Doctrine included pages of annuity and life insurance calculations, prompted by the need to update Edmund Halley’s famous mortality tables. He continued revising the book until, by the final edition, he was too blind to proofread it.7 He might have been too blind to read, but he could see that his book was having a negative impact on society. By demystifying chance, he realized that he was helping to undermine the moral strictures that kept some people away from the gaming tables. In a preface to a later edition, he insisted that “this doctrine is so far from encouraging play that it is rather a guard against it by setting it in a clear light.”

For their frenetic intellectual activity and egalitarian atmosphere, these establishments were called “Penny Universities,” because for the price of a cup of coffee, patrons could hear the latest news, participate in debate, or witness, say, Adam Smith writing his “Wealth of Nations.” If a Londoner was in the mood for science, he could wander over to a place like the Grecian Coffee House, where Isaac Newton, the astronomer Edmond Halley, and the physician Hans Sloane once dissected a dolphin that had wandered into the Thames river. Edification came free with every purchase.
Historians disagree about why the Brits switched so abruptly to tea, terminating the London coffee-house phenomenon, but one possible cause is this: the coffee tasted repulsive. * Since the government taxed coffee by the gallon, proprietors had to make it in advance — first roasting the beans in frying pans over a fire, which left them half scorched and half raw — and then reheat the brew later.

It is an attribute given perhaps to universes, but protected by the limits that exist on how fast information can spread. You can discover whether the Universe is infinite, but the learning will take an infinite time.
THE SHINING
‘Day and night Night and day’
Night and Day, Cole Porter
Fig 7.17 Looking into the woods. Everywhere your line of sight ends on a tree trunk. We should see a forest of stars if we look out into the universe.
Edmond Halley (1656–1742) is known throughout the world because of the comet that bears his name. Halley calculated its orbit and determined that comets seen in 1531, 1607 and 1682 were the same object that followed a 76-year orbit (on average).26 Unfortunately, Halley died in 1742, and never lived to see his prediction come true when the comet returned on Christmas Eve in 1758. Its return is rarely spectacular, but it is one of those events that links the generations.

Dissatisfaction with the Royal Observatory’s performance had come to a head in 1707, with its experts still apparently clueless after more than three decades of research. One foggy night Admiral Sir Clowdisley Shovell, wrongly believing that his fleet was further west of the English mainland, wrecked four ships on the Isles of Scilly. Sir Clowdisley’s miscalculation led to more deaths than the sinking of the Titanic. The British parliament turned to Sir Isaac Newton and the comet expert Edmond Halley for advice, and in 1714 passed the Act of Longitude, promising a prize of £20,000 for a solution to the problem. Compared with the typical wage of the day, this was over £30 million pounds in today’s terms.
The prize transformed the way that the problem of longitude was attacked. No longer were the astronomers of the Royal Observatory the sole official searchers – the answer could come from anyone.

But the complicated behavior of the moon—powerfully influenced as it is by the gravity both of the sun and of the earth—made it much harder to predict its celestial coordinates with accuracy than those of the other heavenly bodies.
Although Newton had dazzled the world with the laws of motion that allowed the paths of the sun and its planets to be predicted with hitherto unimaginable precision, the moon had defeated him. But though his lunar tables were not good enough for the purposes of determining longitude, Edmond Halley (1656–1742) recognized that the errors in them recurred regularly every eighteen years and eleven days—in accordance with a well-known cycle of eclipses. This discovery enabled him to develop a rule for correcting the tables, which was later improved by the French astronomer Pierre-Charles Le Monnier (1715–99). There were still imperfections, but in 1750 another Frenchman, Alexis Claude de Clairaut (1713–65), published a new theory of the moon’s motion in response to a competition launched by the St.

When my colleagues on the navigation team at JPL, for example, want to study a possible trajectory for a new space mission, they load their computers with the positions and masses of the sun, all the planets and their fifty or so large moons, and more than a half million asteroids, to make sure that every single possible “perturber” of the spacecraft is taken into consideration in their calculations. When astronomers and mathematicians like Edmond Halley and Pierre-Simon Laplace were working out the theory of motions of comets and asteroids, they were working on what physicists call the three-body problem, for example needing to account for the gravity and motions of the sun, Jupiter, and one of the Galilean satellites; or maybe the sun, Jupiter, and a newly discovered comet. Today’s more sophisticated computer modeling of solar-system motions search for solutions to what is known as the n-body problem, whereby n is some very large number of objects.

COFFEE HOUSES AND COLLABORATIVE INNOVATION
Hooke and several of his scientific colleagues, including Christopher Wren and Robert Boyle, had acquired a taste for coffee in Oxford during the 1650s, when they had all been members of a club of science enthusiasts formed by John Wilkins, a senior academic at the university. They continued their tradition of coffeehouse discussion in London, where theirs was one of several groups that came together in 1660 to form the Royal Society, Britain’s pioneering scientific institution. The society’s members, who also included Pepys, Isaac Newton, and Edmond Halley, would often decamp to a coffeehouse after its meetings to continue their discussions. On May 7, 1674, for example, Hooke recorded in his diary that he demonstrated an improved form of astronomical quadrant at a meeting of the Royal Society, and then repeated his demonstration afterward at Garraway’s coffeehouse, where he discussed it with John Flamsteed, an astronomer who was appointed by Charles II as the first Astronomer Royal the following year.

They were the only two souls on Earth to witness the 1639 transit. Horrocks’s correction of Kepler’s calculations set the timing for transits in future years. A pair would occur in 1761 and 1769, then in 1874 and 1882, then in the far-off years of 2004 and 2012, continuing on and on in what was thought to be an endless cycle.
Writing in the Proceedings of the Royal Society in 1716, the English astronomer Edmond Halley suggested how Venusian transits could provide an absolute Earthly reference point against which the rest of the universe could be measured. When viewed from different places on Earth, Halley wrote, the path of Venus across the Sun would shift slightly, also shifting the transit’s duration. By precisely timing the transit to distinguish the shift between two widely separated locations, it would be possible to triangulate the distance between the Earth and the Sun.

Isaac Newton is born in England, December 25.
1643 Galileo’s student Evangelista Torricelli (1608-47) invents mercury barometer.
1644 Pope Urban VIII dies.
1648 Thirty Years’ War ends.
1649 Vincenzio Galilei (son) dies in Florence, May 15.
1654 Grand Duke Ferdinando II improves on Galileo’s thermometer by closing the glass tube to keep air out.
1655-56 Christiaan Huygens (1629-95) improves telescope, discovers largest of Saturn’s moons, sees Saturn’s “companions” as a ring, patents pendulum clock.
1659 Suor Arcangela dies at San Matteo, June 14.
1665 Jean-Dominique Cassini (1625-1712) discovers and times the rotation of Jupiter and Mars.
1669 Sestilia Bocchineri Galilei dies.
1670 Grand Duke Ferdinando II dies, succeeded by his only surviving son, Cosimo III.
1676 Ole Roemer (1644-1710) uses eclipses of Jupiter’s moons to determine the speed of light; Cassini discovers gap in Saturn’s rings.
1687 Newton’s laws of motion and universal gravitation are published in his Principia.
1705 Edmond Halley (1656-1742) studies comets, realizes they orbit the Sun, predicts return of a comet later named in his honor.
1714 Daniel Fahrenheit (1686-1736) develops mercury thermometer with accurate scale for scientific purposes.
1718 Halley observes that even the fixed stars move with almost imperceptible “proper motion” over long periods of time.
1728 English astronomer James Bradley (1693-1762) provides first evidence for the Earth’s motion through space based on the aberration of starlight.
1755 Immanuel Kant (1724-1804) discerns the true shape of the Milky Way, identifies the Andromeda nebula as a separate galaxy.
1758 “Halley’s comet” returns.
1761 Mikhail Vasilyevich Lomonosov (1711-65) realizes Venus has an atmosphere.
1771 Comet hunter Charles Messier (1730-1817) identifies a list of noncometary objects, many of which later prove to be distant galaxies.
1781 William Herschel (1738-1822) discovers the planet Uranus.
1810 Napoleon Bonaparte, having conquered the Papal States, transfers the Roman archives, including those of the Holy Office with all records of Galileo’s trial, to Paris.
1822 Holy Office permits publication of books that teach Earth’s motion.
1835 Galileo’s Dialogue is dropped from Index of Prohibited Books.
1838 Stellar parallax, and with it the distance to the stars, is detected independently by astronomers working in South Africa, Russia, and Germany; Friedrich Wilhelm Bessel (1784-1846) publishes the first account of this phenomenon, for the star 61 Cygni.
1843 Galileo’s trial documents are returned to Italy.
1846 Neptune and its largest moon are discovered by predictions and observations of astronomers working in several countries. 1851 Jean-Bernard-Leon Foucault (1819-68) in Paris demonstrates the rotation of the Earth by means of a two-hundred-foot pendulum.
1861 Kingdom of Italy proclaimed, uniting most states and duchies.
1862 French chemist Louis Pasteur (1822-95) publishes germ theory of disease.
1877 Asaph Hall (1829-1907) discovers the moons of Mars.
1890-1910 Complete works, Le Opere di Galileo Galilei, are edited and published in Florence by Antonio Favaro.
1892 University of Pisa awards Galileo an honorary degree—250 years after his death.
1893 Providentissimus Deus of Pope Leo XIII cites Saint Augustine, taking the same position Galileo did in his Letter to Grand Duchess Cristina, to show that the Bible did not aim to teach science.
1894 Pasteur’s student Alexandre Yersin (1863-1943) discovers bubonic plague bacillus and prepares serum to combat it.
1905 Albert Einstein (1879-1955) publishes his special theory of relativity, establishing the speed of light as an absolute limit.
1908 George Ellery Hale (1868-1938) discerns the magnetic nature of sunspots.
1917 Willem de Sitter (1872-1934) intuits the expansion of the universe from Einstein’s equations.
1929 American astronomer Edwin Hubble (1889-1953) finds evidence for expanding universe.
1930 Roberto Cardinal Bellarmino is canonized as Saint Robert Bellarmine by Pope Pius XI.
1935 Pope Pius XI inaugurates Vatican Observatory and Astrophysical Laboratory at Castel Gandolfo.
1950 Humani generis of Pope Pius XII discusses the treatment of unproven scientific theories that may relate to Scripture; reaches same conclusion as Galileo’s Letter to Grand Duchess Cristina.
1959 Unmanned Russian Luna 3 spacecraft radios first views of the Moon’s far side from lunar orbit.
1966 Index of Prohibited Books is abolished following the Second Vatican Council.
1969 American astronauts Neil Armstrong and Buzz Aldrin walk on the Moon.
1971 Apollo 15 commander David R.

This led to Newton presenting his ideas about light and colours to the Society, and in turn to a virulent argument with Robert Hooke (1635–1703), the man who as Curator of Experiments and later Secretary did more than anyone to make the Society a success. The experience confirmed Newton’s view that publicizing his ideas only led to trouble, and he retreated into his shell in Cambridge. There he continued thinking deeply about the nature of the physical world, but stopped telling anyone about his thoughts.
That changed in 1684, when Edmond Halley (1656–1742) visited Newton in Cambridge. The purpose of his visit was to ask if Newton could help with a problem that had been puzzling Halley, Hooke, and another Fellow of the Royal Society, Christopher Wren (1632–1723). The three scientists had realized that the orbits of the planets around the Sun could be explained by a force which falls off in proportion to the square of the distance of a planet from the Sun (an inverse-square law), but they could not prove that all of the laws of planetary motion, described by Johannes Kepler (1571–1630), must result from such a law.

The third volume begins with Newton’s proud statement: “It remains that, from the same principles, I now demonstrate the frame of the system of the world.” The third volume analyzes the diverse phenomena of the real world, the motions of sun and moon, planets, satellites, and comets, the precession of the earth’s axis of rotation, and the rise and fall of tides, and shows how they all occur precisely as his principles predict. The manuscript of the Principia, which Newton’s friend Edmond Halley took with him to London in 1686 to be published, is in Humphrey Newton’s hand.
Humphrey’s description of Newton’s life in Cambridge was written many years later. Newton spent much of his time in the elaboratory, a wooden building in his garden in which he did alchemical experiments. Here is Humphrey writing about Newton as an alchemist:
Especially at spring and fall of the leaf, at which times he used to imploy about six weeks in his Elaboratory, the fire scarcely going out either night or day, he sitting up one night, as I did another, till he had finished his chymical experiments, in the performances of which he was the most accurate, strict, exact.

L’Hôpital’s rule examines 0/0 with tools that were built upon 0/0 to begin with. It is a circular argument. And as physicists and mathematicians all over the world were beginning to use calculus to explain nature, cries of protest emanated from the church.
In 1734, seven years after Newton’s death, an Irish bishop, George Berkeley, wrote a book entitled The Analyst, Or a Discourse Addressed to an Infidel Mathematician. (The mathematician in question was most likely Edmund Halley, always a supporter of Newton.) In The Analyst, Berkeley pounced on Newton’s (and Leibniz’s) dirty tricks with zeros.
Calling infinitesimals “ghosts of departed quantities,” Berkeley showed how making these infinitesimals disappear with impunity can lead to a contradiction. He concluded that “he who can digest a second or third fluxion, a second or third difference, need not, methinks, be squeamish about any point in divinity.”

Books about “experimental” or “natural” philosophy were not new, of course. Newton’s Philosophiæ Naturalis Principia Mathematica had almost instantly revolutionized science when it appeared a century before. As the historian of science Thomas Kuhn writes, “No other work known to the history of science has simultaneously permitted so large an increase in both the scope and precision of research.” The Principia even sold relatively well—Newton and his publisher, Edmund Halley, actually turned a small profit from it, despite its daunting content. But Newton had played by a set of genre conventions that limited the scope of his readership. Like other experimental philosophers of the age, Newton generally adopted a synthetic approach, one that, in the words of the historian Simon Shaffer, “presented discovery as a set of logically inevitable moves, and the achievement of discovery as an heroic act.”

LAW OF UNIVERSAL GRAVITATION (1686)
While the story of Newton’s apple may be the canonical example of private inspiration, the actual origins of the law are much murkier, including a famous battle between Robert Hooke and Newton over who first noted the inverse square relationship that governed the gravitational attraction between two objects.
THREE LAWS OF MOTION AND ORBITS OF COMETS (1687, 1705)
Newton’s three laws of motion were first published in his groundbreaking Philosophioe Naturalis Principia Mathematica in July 1687. Newton’s friend and publisher, Edmund Halley, would then rely on those laws in producing the first accurate prediction of a comet’s orbit around the earth.
PIANO (1700S)
Employed by the Medici court, Bartolomeo Cristofori sought to improve upon the harpsichord and clavichord by creating a similar instrument that would allow the player both expressive control and a larger spectrum of volume. He called it a “pianoforte,” which has since been shortened to “piano.”

But European astronomers were able to observe the transit of Mercury in November that year, vindicating Kepler’s prediction. Eight years later, Englishmen Jeremiah Horrocks and William Crabtree, friends living thirty miles apart, made the frst recorded observations of a Venus transit by projecting the Sun’s image with small telescopes.
Perhaps inspired by a transit of Mercury he observed from the island of St. Helena in 1677, Edmund Halley, of comet fame, presented a paper to the Royal Society in London in 1691 on measuring the distance between the Earth and the Sun—the astronomical unit—using transit timings. His suggestion, an idea also proposed by a Scottish mathematician almost thirty years earlier, was to time the transit from widely separated locations on Earth and use the difference in the apparent paths taken by Venus across the face of the Sun to calculate the Earth-Venus and thus Earth-Sun distance using trigonometry.

When astronomers try to place the moon at a date in
the past when there was known to be an eclipse, their equations often say there was no
such eclipse, or place the eclipse at a different location from where it was observed.
The easiest solution to this problem is to add a small term to the equations of the moon’s
motion that will place the eclipse in the right time and place. The change in motion is
called the “secular acceleration.”
The existence of this acceleration was first suspected by Edmund Halley in 1692,
and was confirmed by astronomers in the eighteenth century.3 An accurate value for
this acceleration is quite important, because without it, it becomes very difficult to
predict the moon’s motion more than a century or two away from the present. Unfortunately calculating this value is rather challenging, as one needs an accurate location
for the moon in the distant past. Reports of historical eclipses provide exactly this
data—when and where the eclipse was seen.

Although the monks probably did not know it, they were competing with the French Enlightenment for the child’s attention. Contemporaries called it the Century of Lights and the Age of Science and Reason, and the popularization of science was its most important intellectual phenomenon. Given the almost dizzying curiosity of the times, it is not surprising that, shortly after his tenth birthday, Pierre Simon was profoundly affected by a spectacular scientific prediction.2
Decades before, the English astronomer Edmond Halley had predicted the reappearance of the long-tailed comet that now bears his name. A trio of French astronomers, Alexis Claude Clairaut, Joseph Lalande, and Nicole-Reine Lepaute, the wife of a celebrated clockmaker, solved a difficult three-body problem and discovered that the gravitational pull of Jupiter and Saturn would delay the arrival of Halley’s comet. The French astronomers accurately pinpointed the date—mid-April 1759 plus or minus a month—when Europeans would be able to see the comet returning from its orbit around the sun.

They just know—without looking at stars, maps, satellites, or scenery, without interrogating anyone or anything. Nor can they be interfered with externally—indeed, the development of inertial navigation was spurred by the need for accurate, jamming-proof guidance systems for missiles.
Flying over north London I can see a churchyard in which I sometimes sit with a coffee, where the tomb of John Harrison, “late of Red-Lion Square,” stands. Encouraged by the astronomer Edmund Halley, Harrison developed the “sea clocks” that helped solve the longitude problem, the difficulty with determining one’s east–west position at sea, an achievement so important that the officials who recognized it were known as Commissioners of Longitude. At such moments over London, as we come to the end of the planetwide countdown that every flight to this city effects, our longitude is nearly zero; it may ticktock from west and east and back to west as we cross the Greenwich Meridian in the next minutes of our approach pattern to Heathrow.

And so their ships passed, moving apart like floating islands, Tupaia taking with him his perfect knowledge of the Pacific, and Cook looking away, in hot pursuit of the key to self-centering, a quest that would culminate in GPS.
CHAPTER TWO
The When and the Where
When James Cook visited Tahiti in 1769, the summer he met Tupaia, the captain was moonlighting as a stargazer. Every dozen decades or so, the planet Venus crosses the face of the sun—usually twice within a period of a few years—a phenomenon called the transit of Venus. In the late seventeenth century, the astronomer Edmund Halley had argued that close observation of the transit could help refine calculations regarding the distance between Earth, moon, sun, and other planets. These calculations would be more accurate, he noted, if observations were taken from around the world. Several worldwide expeditions had been dispatched for the 1761 transit, but the next, in 1769, involved a much larger global effort. Cook’s would be one of about 120 simultaneous observations, organized by several countries, with the results compiled and analyzed by astronomers in Paris.

In 1720, as the Mississippi Company’s shares rose, it issued more notes, which purchased more shares, increasing its price still more. Vast paper fortunes were made, and the word millionaire was coined. The frenzy spilled over the entire continent, where new ventures were floated with the vast amounts of capital now available.
There was even a fashionable new technology involved: the laws of probability. Fermat and Pascal had recently invented this branch of mathematics, and, in 1693, Astronomer Royal Edmund Halley developed the first mortality tables. Soon the formation of insurance companies became all the rage; these would figure prominently as the speculative action moved to London.
The ancien régime was not the only government deep in hock. By 1719, England had incurred immense debts during the War of the Spanish Succession. In fact, a decade before, in 1710, the South Sea Company had actually exchanged government debt held by investors for its shares and had been granted the right to a monopoly on trade with the Spanish Empire in America.

In the same year that Ars Cogitandi appeared (1662), John Graunt published his ‘Natural and Political Observations . . . Made upon the Bills of Mortality’, which sought to estimate the likelihood of dying from a particular cause on the basis of official London mortality statistics. However, Graunt’s data did not include ages at death, limiting what could legitimately be inferred from them. It was his fellow member of the Royal Society, Edmund Halley, who made the critical breakthrough using data supplied to the Society from the Prussian town of Breslau (today Wrocław in Poland). Halley’s life table, based on 1,238 recorded births and 1,174 recorded deaths, gives the odds of not dying in a given year: ‘It being 100 to 1 that a Man of 20 dies not in a year, and but 38 to 1 for a Man of 50 . . .’ This was to be one of the founding stones of actuarial mathematics. 17
3.

Sampling, averages, and notions of what is normal make up the struc ture that would in time house the science of statistical analysis, putting information into the service of decision-making and influencing the degrees of belief we hold about the probabilities of future events.
Some thirty years after the publication of Graunt's Natural and Political Observations, another work appeared that was similar to Graunt's but even more important to the history of risk management. The author of this work, Edmund Halley, was a scientist of high repute who was familiar with Graunt's work and was able to carry his analysis further. Without Graunt's first effort, however, the idea of such a study might never have occurred to Halley.
Although Halley was English, the data he used came from the Silesian town of Breslau-Breslaw, as it was spelled in those dayslocated in the easternmost part of Germany; since the Second World War the town has been part of Poland and is now known as Wrozlaw.

The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers.6
Hooke wrote to Newton about his speculations, including the inverse square law. Newton brushed him off, replying that he had not heard of Hooke’s work, and that the “method of indivisibles”7 (that is, calculus) was needed to understand planetary motions.
Then in August 1684 Newton received a fateful visit in Cambridge from the astronomer Edmund Halley. Like Newton and Hooke and also Wren, Halley had seen the connection between the inverse square law of gravitation and Kepler’s third law for circular orbits. Halley asked Newton what would be the actual shape of the orbit of a body moving under the influence of a force that decreases with the inverse square of the distance. Newton answered that the orbit would be an ellipse, and promised to send a proof.

In addition to assessing the ingredients of a star, they demonstrated how spectroscopy could be used to measure a star’s velocity.
Following Galileo, astronomers had assumed that the stars were stationary. Although the stars all moved across the sky every night, astronomers realised that this apparent motion was caused by the Earth’s rotation. In particular, they assumed that the stars’ positions relative to one another remained the same. In fact, this was false, as pointed out in 1718 by the English astronomer Edmund Halley. Even after taking into account the motion of the Earth, he became aware of subtle discrepancies in the recorded positions of the stars Sirius, Arcturus and Procyon compared with measurements made by Ptolemy many centuries earlier. Halley realised that these differences were not down to inaccurate measurements, but were the result of genuine shifts in the positions of these stars over time.
With infinitely precise measuring tools and infinitely powerful telescopes, astronomers would have been able to detect the so-called proper motion of every star, but in reality the stars change position so gradually that even modern astronomers can barely detect shifts in stellar positions.

The array of inhabitants and visitors produced bewildering complications: there was no island currency, and at one time a treasurer complained that among the coinage in common use in Jamestown were gold dubloons, mohurs from Bengal, moidores, star pagodas, gold gubbers and Venetian sequins, as well as rupees and ducatoons, German crowns, Marie Thérèse dollars, joes from Portugal, guilders from Holland, rixdollars, francs and English shillings.
A steady cavalcade of the distinguished dropped by: Edmund Halley, the astronomer who gave his name to the comet, came to the mountains of St Helena to observe the transit of Mercury; fog obscured his view, and it often swirls over the flax-covered hill that bears his name, and where he mounted his telescope. Captain Bligh looked in, and presented some breadfruit which he was taking from Tahiti to Jamaica. Captain Cook, on his way back from Antarctica, spent a few days on the island, and made some pointed criticisms of the islanders’ agricultural methods.

pages: 464words: 139,088

The End of Alchemy: Money, Banking and the Future of the Global Economy
by
Mervyn King

Newspapers and television are only too willing to print the latest forecast of, say, national income with a degree of precision that beggars belief and far exceeds the ability of statisticians to measure it. And at the end of each year prizes are awarded to the forecasters who turned out to be the most accurate. It makes as much sense as it would to award the Fields Medal in mathematics to the winner of the National Lottery.
No economic forecaster has ever been able to match Edmund Halley, who in 1682 made calculations predicting that the comet then visible in the skies would return seventy-six years later. It did – on Christmas Day 1758. Fortunately the length of the economic cycle – the duration of the expansion and subsequent contraction of the economy before it returns to its normal levels of output and employment – is shorter than the periodicity of Halley’s Comet – although if it goes on increasing at its present rate even that might not be true.

Many of the most pressing problems of the age – philosophical as well as political and military – concerned the sea. The problem of the longitude is only the best known of them: anyone who furnished a reliable and portable technique for determining the longitude of a ship far removed from its home port would become rich, and would vastly enhance the power of the nation that possessed the secret. Aspirants to “solve the longitude” included not only men like Edmond Halley but any number of otherwise obscure “projectors.” By the early eighteenth century they had become a running joke. But as well as the longitude, the sea presented other issues demanding explanation, including the phenomena of the tides. Alongside these issues, moreover, which were predominantly mathematical and physical, it also posed a set of chemical questions. Those questions concerned the origin, composition, and possible utility of seawater.

The plays that Jeter had to dive for, a truly great defensive shortstop like Ozzie Smith might have made easily—perhaps receiving less credit for them because he made them look routine.
FIGURE C-1: SHORTSTOP DIVING RANGES
Whatever range of abilities we have acquired, there will always be tasks sitting right at the edge of them. If we judge ourselves by what is hardest for us, we may take for granted those things that we do easily and routinely.
One of the most spectacularly correct predictions in history was that of the English astronomer Edmund Halley, who in 1705 predicted that a great comet would return to the earth in 1758. Halley had many doubters, but the comet returned just in the nick of time.2 Comets, which in antiquity were regarded as being wholly unpredictable omens from the gods,3 are now seen as uncannily regular and predictable things.
Astronomers predict that Halley’s Comet will next make its closest approach to the earth on July 28, 2061.

I wrote today to Hanover, booked my observations and made a fair copy of 3 letters…The night is cloudy. August 5th. I calculated nebulae all day, paid the smith…The night was tolerably fine and I SAW THE COMET.22
Both Aristotle and Galileo had thought comets were low-level atmospheric phenomena, perhaps lower than the moon. The study of comets was improved by the sixteenth-century Danish astronomer Tycho Brahe, but transformed in 1682 when Edmund Halley famously calculated that the Great Comet of that year, subsequently named after him, would reappear in 1759. It was then finally accepted that comets were outer-space objects that moved in extreme elliptical orbits round the sun, and swung far beyond the known planets. Yet they were still mysterious: of unknown origin and composition, various in their appearance, irregular and alarming in their habits.

Although he admired many of its members, the dour Wood was contemptuous of the Oxford Coffee Club itself, perhaps because he had little interest in the scientific topics that furnished the subjects for its discussions. He evidently believed, in this case at least, that the whole was less than the sum of its illustrious parts, because he derisively records in his history that a club was built, “at Tillyards, where many pretended wits would meet and deride all others.” The first participants included Hans Sloane, founder of the British Museum, Sir Edmund Halley, the great astronomer, and Sir Isaac Newton, originator of the calculus, celestial mechanics, and the postulates of classical physics. The members’ avid curiosity prompted hands-on scientific investigation: Sloane, Halley, and Newton are said to have dissected a dolphin on a table in the coffeehouse before an amazed audience.
The Oxford Coffee Club quickly absorbed the membership of a competing science club, which had been set up concurrently by an Oxford tutor, Peter Sthael of Strasbourg.

In Italy, the impact of Newton can be measured by the appearance in 1737 of Il Newtonianismo per le Dame (Newtonism for Ladies) by Francesco Algarotti (Mazzotti, 2004).22 Over time, Newton’s standing only rose as the embodiment of the Enlightenment’s view of the ideal scientist.23 The impact of Newton on the thin but strategically placed class of European intellectuals in the eighteenth century was immense and was famously summarized by Alexander Pope’s epitaph.24 Similarly, the astronomer Edmund Halley in his “Ode to Newton” (1687) wrote “Come celebrate with me in song the name of Newton, to the Muses dear; for he Unlocked the hidden treasuries of Truth. … Nearer the Gods, no mortal may approach” (Halley [1687], 1934]).
The only other intellectual of the age whose impact on his age and stature in modern assessment resembles Newton’s (despite differing from him in almost every other dimension), John Locke, recognized Newton’s achievement—but only after verifying with Huygens that the mathematics were sound.25 The respectability of scientific research that augments useful knowledge was embodied in the Royal Society that Newton presided over.

What he asked of me seemed harmless—so I did it.”
“What did you and this man talk about when you met in the pub?” asked Orney.
“He was an educated Frenchman. He professed to be a sort of Enthusiast, an amateur of Natural Philosophy. He simply wanted to know what the Royal Society was like. He asked all sorts of questions about what happened during the meetings, and what the Fellows were like—Sir Christopher Wren, Edmund Halley, and especially Sir Isaac Newton.”
“Did you ever mention to this amateur that Sir Isaac made a practice of coming to Crane Court on Sunday evenings, and working late?” asked Daniel.
“I don’t remember for certain, sir, but it is quite possible—that is the sort of thing this fellow loved to hear about, sir.” Arlanc then paused, for everyone in the room had exhaled, and some who’d been studying his phizz for the last several minutes were now looking at their fingernails or gazing out the window.